Heretofore, such a multi-speed sprocket assembly comprising two or more sprockets has been well known. A derailleur separate from the sprocket assembly is operated to move a driving chain axially of the sprockets and switch it to a desired sprocket, thereby transmitting a pedalling driving force to a rear wheel hub at the predetermined speed-change ratio.
In order to increase the speed-change ratio, it is enough to increase the difference between the numbers of teeth at the smaller diameter sprocket and the larger diameter sprocket, of the multi-speed sprocket assembly. However, a difference of three or more teeth makes a radius of the addendum circle of the smaller diameter sprocket smaller than a radius of the dedendum circle of the larger diameter sprocket, so that the radial length between the addendum circles of both the sprockets becomes too large making it difficult to switch the chain quickly and smoothly to the desired sprocket. In other words, the driving chain, when switched from the smaller diameter sprocket to the larger diameter sprocket, contacts, prior to engagement with one tooth thereof, a tooth adjacent to and ahead of the one tooth in the direction of normal rotation of the sprocket. Hence, it is difficult to smoothly shift the chain axially outwardly of the larger diameter sprocket for ensuring engagement therewith, resulting in idling of the sprocket. The chain, when switched from the larger diameter sprocket to the smaller diameter sprocket, is intended to disengage from the larger diameter sprocket, but interferes with a tooth thereof positioned behind a tooth ready to disengage the chain, in the direction of normal rotation of the larger diameter sprocket. The chain does not smoothly shift to the smaller diameter sprocket, resulting in unreliable disengagement of the chain from the larger diameter sprocket.
Also, the speed-change ratio, when increased, makes the sprocket ratio larger considerably increasing variations in torque when switching the chain, so that a rider is subjected to a great impact against pedalling to happen to miss his treading on the pedal, which is very dangerous for him.